Blake Adam Fleisig, 35, and Anna Christine Koosmann, 36, were onboard Delta Flight 2565 to Los Angeles on Wednesday night (December 28), when the incident happened.
But when the flight landed back at Minneapolis-St Paul Airport in the US, things got even more nasty.
Police officers are seen leading the pair through the aisles and out of the plane.
Fellow passengers are heard cheering, which prompts Fleisig – who is the Vice President of Internal Audit Treasury Finance at CitiBank – to attack one person.
Officers desperately try and pull the man off the passenger, as onlookers scream “Stop, stop, stop!”
Another passenger is heard saying: “Just let them get off the plane.”
Finally, the police get the situation under control and the couple carry on their walk to the plane’s exit.
Koosmann then suddenly screams: “You better f*** your sucking…”
“You’re already going to jail,” one of the cops tells her to which she replies “for what?”
In a statement to Mail Online, Delta said the passengers had “refused to follow crew instructions, became aggressive and created a disruption in the cabin.”
Delta Flight 2565 arrived in Los Angeles two hours and 34 minutes behind schedule, according to FlightAware.
Fleisig was arrested without resistance and faces one charge of disorderly conduct with brawling or fighting.
He was released on Wednesday night (December 28).
Koosmann was also charged with disorderly conduct and remains in custody at the Hennepin County Detention Centre in Minneapolis.
Both airport police and the FBI are investigating the incident.